It is possible to climb both Lhotse & Everest in one expedition, but this is extremely rare. Anatoli Boukreev achieved this feat in 1996 after the infamous storm which claimed 8 lives. After an ascent of Everest because your body is acclimatised to the altitide it is possible to ascend back through the icefall and through the western cwm up Lhotse in quick time. However you would need to be incredibly determined and fit to achieve two 8000 metre summits on one expedition.

Its achievable but difficult.

Most expedions which camp at Base Camp on the Khumbu glacier will attempt either Everest or Lhotse, not both together. It is hard enough just getting up one of them let alone two.

You need to go back down to basecamp if you want the second summit to count (technically, because you would still be standing on top of the mountain!!!). Because you need the mountain to be climbed from basecamp to the summit. And btw it is not considered a secondary peak because of the distance that separates it from Everest.

if that is the case, does it mean that we can summit two 8000ers at one go? summit Lhotse, then Everest or vice versa.

No one has ever climbed Lhotse via the South Col. The route is too difficult. You would have to descend and climb the couloir above the Lhotse Face.

You need to go back down to basecamp if you want the second summit to count (technically, because you would still be standing on top of the mountain!!!).

I disagree. You would have to descend down the Lhotse Face quite aways from the South Col anyway to climb Lhotse, and if you did do it from the South Col, you would have solved one of the problems on the "Everest Horseshoe". Anyone doing that deserves a huge amount of credit and could certainly count it.